cp's OEIS Frontend

A323437 Number of semistandard Young tableaux whose entries are the prime indices of n.

%I A323437 #7 Feb 03 2021 07:44:35
%S A323437 1,1,1,1,1,1,2,1,1,1,2,1,2,1,2,2,1,1,2,1,2,2,2,1,2,1,2,1,2,1,4,1,1,2,
%T A323437 2,2,3,1,2,2,2,1,4,1,2,2,2,1,2,1,2,2,2,1,2,2,2,2,2,1,5,1,2,2,1,2,4,1,
%U A323437 2,2,4,1,3,1,2,2,2,2,4,1,2,1,2,1,5,2,2,2
%N A323437 Number of semistandard Young tableaux whose entries are the prime indices of n.
%C A323437 Number of ways to fill a Young diagram with the prime indices of n such that all rows are weakly increasing and all columns are strictly increasing.
%C A323437 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A323437 Is this a duplicate of A339887? - _R. J. Mathar_, Feb 03 2021
%F A323437 Sum_{A056239(n) = k} a(k) = A003293(n).
%e A323437 The a(60) = 5 tableaux:
%e A323437   1123
%e A323437 .
%e A323437   11   112   113
%e A323437   23   3     2
%e A323437 .
%e A323437   11
%e A323437   2
%e A323437   3
%t A323437 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A323437 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A323437 ptnplane[n_]:=Union[Map[primeMS,Join@@Permutations/@facs[n],{2}]];
%t A323437 Table[Length[Select[ptnplane[y],And[And@@Less@@@#,And@@(LessEqual@@@Transpose[PadRight[#]/.(0->Infinity)])]&]],{y,100}]
%Y A323437 Cf. A000085, A000219, A003293, A053529, A056239, A112798, A138178, A153452, A296188.
%Y A323437 Cf. A323300, A323429, A323432, A323436, A323438, A323439.
%K A323437 nonn
%O A323437 0,7
%A A323437 _Gus Wiseman_, Jan 15 2019